Abstract: We considered an initial value problem of elliptic equation. This problem is severely illposed, so we must use regularization in the solving process. When the spectrum of the operator consided here satisfied some proper conditions, we made use of a specific form of spectrum decomposition to decompose the solution, and introduced a regularization method in a specifical subspace. We used this method to develop a numerical computation for an initial value problem of Laplace equation. The numerical experiments demonstrate that this method is efficient.

Key words: elliptic equation, illposed problem, regularization method, numerical solution of differential equation 